1. The equation y equals , 5 sevenths , x describes a proportional relationship between x and y. What is the constant of proportionality?
2. The equation P = 3s represents the perimeter P of an equilateral triangle with side length s. What is the perimeter of an equilateral triangle with side length 4 ft?
3. You bike 11.2 miles in 1.4 hours at a steady rate. What equation represents the proportional relationship between the x hours you bike and the distance y in miles that you travel?
4. Marco needs to buy some cat food. At the nearest store, 3 bags of cat food cost $15.75. How much would Marco spend on 5 bags of cat food?
5. An arts and crafts store sells sheets of stickers. Use the table to write an equation you can use to find the total cost y in dollars for x sheets of stickers.
6. Jane likes to exercise daily. The table shows the number of calories y she burns by exercising steadily for x minutes. How many calories would she burn by exercising for 29 minutes?
7. Solve the proportion 22 over 24 , equals , t over 84
8. In a certain chemical, the ratio of zinc to copper is 3 to 16. A jar of the chemical contains 320 grams of copper. How many grams of zinc does it contain?
9. Mental Math Professional chefs usually measure ingredients by weight rather than by volume. A recipe calls for 2 ounces of flour for every 3 ounces of sugar.
a. If you are a chef and you use 12 ounces of sugar, how many ounces of flour should you use?
b. Explain how you can use mental math to find the answer. Explain why a chef might need mental math to find an answer like this.
10. Writing Ann's car can go 228 miles on 6 gallons of gas. During a drive last weekend, Ann used 7 gallons of gas.
a. How far did she drive?
b. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.
11. Reasoning The equation y = 6.41x describes a proportional relationship between x and y.
a. What is the constant of proportionality?
b. Explain why your answer is called the “constant of proportionality.”
12. Multiple Representations The proportions eh over b , equals , c over d and b over eh , equals , d over c are called equivalent proportions.
a. Find a proportion equivalent to 3 sevenths , equals , 9 over x , .
A. 7 thirds , equals , 9 over x
B. 7 thirds , equals , x over 9
C. 7 ninths , equals , x over 3
D. 7 over x , equals , 9 thirds
b. What is the solution of the proportion?
c. Explain why, based on this example, solving an equivalent proportion can be useful.